In the present research, laser micro machining (LMM) of tungsten-molybdenum general purpose high speed steel (Rex M2) has been studied. Selection of optimum machining parameter combinations for obtaining higher depth of groove and smaller height of recast layer is a challenging task in LMM due to the presence of a large number of process variables. There is no perfect combination of parameters which can simultaneously result in both the highest depth of groove and lowest height of recast layer. This paper presents an attempt to develop a strategy for predicting the optimum machining parameter setting for the generation of the maximum depth of groove with minimum height of recast layer. A feed forward back-propagation neural network has been developed to model the machining process. The model, after proper training, is capable of predicting the response parameters as a function of four different control parameters. Experimental results demonstrate that the machining model is suitable and the optimization strategy satisfies practical requirements. The developed model has been found to be quite unique, powerful and flexible.